Can't apply modifiers with shapekeys on blender 2.8
Lets say we have a mesh with 2 shapekeys: 1 basis and 2nd Big Ears.

Create a copy of the mesh, select the copy and delete the basis shape key, then the big ears shape key.

Select the original and delete the big ears shape key, then the basis; you'll end up with two different meshes, one original and one deformed.

Apply your modifiers in both the objects (starting from the upper in the stack).

Then create a basis shape key for the original mesh, select the deformed, shift select the original and use the "Join as shapes" function.